用于多原子气体DSMC模拟中方差缩减的实用偏差粒子方法
Practical deviational particle method for variance reduction in polyatomic gas DSMC simulations
AI总结：
本研究针对多原子气体DSMC模拟计算成本高的问题，提出结合LVDSMC方法与Larsen-Borgnakke模型的实用偏差粒子方法，引入非弹性碰撞分组缩减算法，可将方差降至DSMC的约5%，实现宽非平衡范围的高效准确模拟。
摘要：
直接模拟蒙特卡洛（DSMC）方法是求解玻尔兹曼方程的一种广泛使用的随机粒子方法。然而，其计算成本仍是主要缺陷，这可归因于处理低马赫数流动时的统计误差。因此，许多研究聚焦于方差缩减以降低计算成本。其中一种方法是偏差粒子（DP）方法，该方法仅对偏离平衡态的部分进行建模。DP方法已在低方差偏差模拟蒙特卡洛（LVDSMC）方法中实现，已被证明对单原子气体模拟有效，但在扩展至多原子气体时面临局限。本研究中，我们提出了一种适用于多原子气体模拟的实用DP方法，该方法将LVDSMC方法与Larsen-Borgnakke（LB）模型相结合，针对非弹性碰撞过程引入了分组缩减算法。数值实验表明，所提方法可在较宽的非平衡值范围内高效且准确地模拟流动。值得注意的是，其方差降至DSMC方法的约5%。
英文摘要：
The direct simulation Monte Carlo (DSMC) method is a widely used stochastic particle approach to solving the Boltzmann equation. However, its computational cost remains a major drawback, which can be attributed to statistical errors when handling flows with low Mach numbers. Thus, many studies have focused on variance reduction to reduce the computational cost. One approach is the deviational particle (DP) method, which focuses solely on modeling deviations from the equilibrium state. The DP method has been implemented in the low-variance deviational simulation Monte Carlo (LVDSMC) method, which has proven effective for monatomic gas simulations but faces limitations when extended to polyatomic gases. In this study, we present a practical DP method for polyatomic gas simulations that combines the LVDSMC method with the Larsen-Borgnakke (LB) model, which introduces a group reduction algorithm for the inelastic collision process. Numerical experiments demonstrated that the proposed method efficiently and accurately simulates flows across a relatively broad range of non-equilibrium values. Remarkably, the variance was reduced to about 5% that of the DSMC method.
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